Linear Programming Help Center

Learn more

Warning: The hard deadline has passed. You can attempt it, but you will not get credit for it. You are welcome to try it as a learning exercise.

To specify an array or sequence of values in an answer, separate the values in
the sequence by whitespace. For example, if the question asks for the first
ten powers of two (starting at 1), then the following answer is acceptable:

     1 2 4 8 16 32 64 128 256 512

If you wish to discuss a particular question and answer in the forums, please
post the entire question and answer, including the seed (which can be used by
the course staff to uniquely identify the question) and the explanation (which
contains the correct answer).

Question 1

(seed = 203281)
Which of the following problems can be reduced to linear programming? Check all that apply.

Question 2

(seed = 519841)
Consider the following linear programming simplex tableaux with 3 equations and 8 variables:

    maximize Z
     +    2 x0  +    3 x1             -    2 x3                        -  8/5 x6  -  1/4 x7    -  Z    = -354
    ---------------------------------------------------------------------------------------------------------
     -  8/5 x0  +    8 x1  +    1 x2  -  5/4 x3                        -    3 x6  +  5/4 x7            =   18
     +   10 x0  +  9/2 x1             -    3 x3  +    1 x4             -  8/5 x6  +  4/5 x7            =   42
     +    8 x0  +    1 x1             -  5/2 x3             +    1 x5  +    2 x6  -  1/3 x7            =   54
            x0  ,      x1  ,      x2  ,      x3  ,      x4  ,      x5  ,      x6  ,      x7           >=    0


Which variable could be the next to *enter* the basis? Check all that apply.

Question 3

(seed = 765245)
Consider the following linear programming simplex tableaux with 5 equations and 9 variables:

    maximize Z
                -  1/2 x1  -    3 x2  +  1/3 x3                                              -  5/2 x8    -  Z    = -156
    --------------------------------------------------------------------------------------------------------------------
                -  7/4 x1  -    2 x2  +  3/2 x3                                   +    1 x7  +  1/2 x8            =   24
                +  5/3 x1  -  2/5 x2  -    6 x3  +    1 x4                                   -  7/3 x8            =   18
                -  4/3 x1  +    2 x2  +    4 x3             +    1 x5                        +  3/2 x8            =   54
     +    1 x0  +  1/4 x1  -    3 x2  +  9/4 x3                                              +  5/3 x8            =   18
                +  4/5 x1  -    9 x2  +    7 x3                        +    1 x6             -  2/5 x8            =   60
            x0  ,      x1  ,      x2  ,      x3  ,      x4  ,      x5  ,      x6  ,      x7  ,      x8           >=    0


Suppose that variable x3 is the variable chosen to enter the basis.
Which variable or variables could be the next to *leave* the basis? Check all that apply.
    
You cannot submit your work until you agree to the Honor Code. Thanks!